Question

Let U, the universal set, consist of all the positive rational numbers (or fractions).

Let A be the set defined by A = {p/q | p,q are odd naturals and q is nonzero}.

Find a set B that satisfied the following 3 conditions:

1) B is a subset of A', the complement of A.

2) B has exactly 255 proper subsets.

3) No element of B is greater than 1.

Answer 1

well, 8 elements are in set B, since to have 255 proper subsets, the set must contain n elements where 2^n-1=255

Answer 2

so any 8 fractions p/q which where p,q are even naturals and q is nonzero would work

Answer 3

and p<q

Answer 4

how do you know what set b is? and how there are 8 elements?

Answer 5

B has exactly 255 proper subsets. implies there are 8 elements

Answer 6

set B could be any set, since the question states that Find a set B that satisfied the following 3 conditions:

Answer 7

so how do i find set b?

Answer 8

any set with 8 fractions p/q where either p or q are not odd naturals and q is nonzero and p<q
example {1/3,3/5,5/7,7/9,9/11,11/13,13/15,15/17}

Answer 9

ok so thats the answer to the question all these fractions?

Answer 10

yep, any other 8 fractions that satisfy the description would also work

Answer 11

ok great what does is mean that b is the subset of a '?

Answer 12

yes, B is the subset of A' which is the compliment of A

Answer 13

but what does that have to do with the question?

Answer 14

The questions is asking you to find a subset of A', that has 8 elements, and each element is less than 1

Answer 15

and all elements have to be positive rational numbers since B is also a subset of U

Answer 16

ok thank you for your help!! i really appreciate it!

Answer 17

np